Hard to answer such a broad question.

Take Sunshine for example. It was made for about 30,000,000 dollars, which for a big sci-fi movie is very little. However, the effects look like the work of a much larger production.

Several years ago I made a 30 minute movie with a MiniDV camera which cost about 300 dollars. We used wooded locations, used few props (this was a medieval setting), and the "actors", including myself, were all unpaid because it was for fun. Premiere Elements cost 100 dollars, and with all of the supplies the production probably ran close to a thousand dollars. The movie was pretty shit, but with a better script it would probably have been watchable. So a thousand dollars doesn't buy that much in terms of quality.

To cover the basics, hire people with acting experience, write a good script, and get permission to film in interesting locations. The costs of shooting digital should be very small compared to what is in front of the camera. Anyone can create passable CG sequences these days, the trick is primarily in story, secondly in acting.

If you want to know what it takes to make a good movie on the cheap, look at The Movie Hero. That is one of my favorite movies, and it uses extremely little in the way of sets and effects.